Pao-Hsiung Chiu

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In this paper a conservative phase-field method based on the work of Sun and Beckermann [Y. Sun, C. Beckermann, Sharp interface tracking using the phase-field equation, J. Comput. Phys. 220 (2007) 626–653] for solving the twoand three-dimensional two-phase incompressible Navier–Stokes equations is proposed. The present method can preserve the total mass as(More)
The paper presents an iterative algorithm for studying a nonlinear shallow-water wave equation. The equation is written as an evolution equation, involving only first-order spatial derivatives, coupled with the Helmholtz equation. We propose a two-step iterative method that first solves the evolution equation by the implicit midpoint rule and then solves(More)
A two-step interface capturing scheme, implemented within the framework of conservative level set method, is developed in this study to simulate the gas/water two-phase fluid flow. In addition to solving the pure advection equation, which is used to advect the level set function for tracking interface, both nonlinear and stabilized features are taken into(More)
We investigate solution properties of a class of evolutionary partial differential equations (PDEs) with viscous and inviscid regularization. An equation in this class of PDEs can be written as an evolution equation, involving only first-order spatial derivatives, coupled with the Helmholtz equation. A recently developed two-step iterative method (Chiu et(More)
The paper presents a sixth-order numerical algorithm for studying the completely integrable CamassHolm (CH) equation. The proposed sixth-order accurate method preserves both the dispersion relation and the Hamiltonians of the CH equation. The CH equation in this study is written as an evolution equation, involving only the first-order spatial derivatives,(More)
We present a particle method for studying a quasilinear partial differential equation (PDE) in a class proposed for the regularization of the Hopf (inviscid Burger) equation via nonlinear dispersion-like terms. These are obtained in an advection equation by coupling the advecting field to the advected one through a Helmholtz operator. Solutions of this PDE(More)